The generator matrix

 1  0  0  0  1  1  1  1  4  0  1  1  1  6
 0  1  0  0  0  4  1  3  1  1  1  6  5  1
 0  0  1  0  1  2  6  3  5  0  5  6  4  7
 0  0  0  1  1  3  2  7  6  3  0  4  2  5
 0  0  0  0  4  0  0  0  0  4  4  4  0  4

generates a code of length 14 over Z8 who´s minimum homogenous weight is 10.

Homogenous weight enumerator: w(x)=1x^0+268x^10+484x^11+1029x^12+1424x^13+1711x^14+1496x^15+1133x^16+400x^17+194x^18+36x^19+13x^20+3x^22

The gray image is a code over GF(2) with n=56, k=13 and d=20.
This code was found by Heurico 1.11 in 0.406 seconds.